Emergency services were called to the northbound carriageway of the road, close to junction 39, at around 7.50am this morning.
Police said a blue Ford Mondeo and a white Kia Picanto had been involved in a collision.
Crews from South Kirkby fire station said they freed the woman, who had become trapped in one of the vehicles.
Firefighter Daniel Hornsby said she had two dogs in the car with her, one of which died in the crash.
He said: “There were two walking wounded at the scene, one deceased dog and one very poorly dog. We had to extricate one female from one of the cars by taking the roof off.”
The lady was taken to Pinderfields Hospital by ambulance.
A police spokeswoman said: “There appears to be minor injuries.”
The carriageway was shut whilst emergency teams dealt with the incident, but it re-opened at 9.10am.